Genuine Spin-Flip in Binary Black Holes

We perform a full numerical simulation of binary spinning black holes to display the long term spin dynamics. We start the simulation at an initial proper separation between the equal mass holes of $d\approx25M$ and evolve them down to merger for nearly 48 orbits, 3 precession cycles and half of a flip-flop cycle. The simulation lasts for $t=20000M$ and displays a change in the orientation of the spin of the black holes with one of them going from initially aligned with the orbital angular momentum to a complete anti-alignment after half of a flip-flop cycle. We compare this evolution with an integration of the 3.5 Post-Newtonian equations of motion and spin evolution to show that this process continuously flip-flops the spin during the lifetime of the binary until merger. We also provide lower order analytic expressions for the maximum flip-flop angle and frequency. We discuss the effects on spin growth in accreting binaries and the observational consequences for galactic and supermassive binary black holes.